Cluster extraction and annotation strategies on tabular datasets with diverse feature types¶

Importing necessary libraries¶

In [1]:
import numpy as np
import pandas as pd
from sklearn.preprocessing import StandardScaler
import matplotlib.pyplot as plt
import seaborn as sns
%matplotlib inline
import warnings
warnings.filterwarnings('ignore')
import tensorflow as tf
from tensorflow import keras
import umap.umap_ as umap
%config InlineBackend.figure_format = 'svg'

Importing pre-processed data¶

In [2]:
np.random.seed(42)
pd.set_option('display.max_columns', None)
pd.set_option('display.max_rows', 100)
data=pd.read_csv('Preprocessed_DM_xx.csv')
In [3]:
np.random.seed(42)
data=data.sample(frac=1) #Shuffle the data set

Feature engineering¶

  • Creating new feature called hypertension
  • Filtering unnecessary details
In [4]:
np.random.seed(42)
HTN_indexes=data.loc[(data['Currently.taking.a.prescribed.medicine.to.lower.BP'] != 0) | (data['First.SYSTOLIC.reading'] >= 140) | (data['First.DIASTOLIC.reading'] >= 90) ].index.values
HTN_cols=np.zeros(data.shape[0])
HTN_cols[[HTN_indexes]]=1
data['HTN']=HTN_cols
data=data.drop(["First.SYSTOLIC.reading","First.DIASTOLIC.reading","Currently.taking.a.prescribed.medicine.to.lower.BP"], axis=1)
data=data.reset_index(drop=True)
data.columns
data=data.drop(["Hb_adjust_alt_smok","Second.SYSTOLIC.reading","Second.DIASTOLIC.reading","Third.SYSTOLIC.reading","Third.DIASTOLIC.reading","Hb_status","Glucose.level",'SBP_status'], axis=1)
data=data.loc[data['BMI'] != 99.99]
data=data.loc[data['Hemoglobin.level..g.dl...1.decimal.'] != 99.99]
data=data.loc[data['Currently.has.asthma'] != .5]
data=data.loc[data['Currently.has.thyroid.disorder'] != .5]
data=data.loc[data['Currently.has.heart.disease'] != .5]
data=data.loc[data['Currently.has.cancer'] != .5]
data=data.loc[data['DM_history'] == 1]
data=data.loc[data['Type.of.caste.or.tribe.of.the.household.head'] != 0]
data=data.loc[data['Time.to.get.to.water.source..minutes.'] != -1]
data=data.drop(["Unnamed: 0","DM_status","DM_history"], axis=1)
In [5]:
np.random.seed(42)
i=[x for x in range(10125)]

data.set_index(pd.Series(i), inplace=True) # Reset the index

Spliting features¶

Creating 2 new dataframes: "data_disease" with features related to disease and "data_others" with rest of the features

In [6]:
data_disease= data[['Currently.has.asthma',
       'Currently.has.thyroid.disorder', 'Currently.has.heart.disease',
       'Currently.has.cancer', 'Suffers.from.TB','HTN']]
In [7]:
data_others= data[['Drinks.alcohol', 'Smoking_stat','Has.refrigerator',
       'Has.bicycle', 'Has.motorcycle.scooter', 'Has.car.truck', 'Owns.livestock..herds.or.farm.animals','Frequency.takes.milk.or.curd',
       'Frequency.eats.pulses.or.beans',
       'Frequency.eats.dark.green.leafy.vegetable', 'Frequency.eats.fruits',
       'Frequency.eats.eggs', 'Frequency.eats.fish',
       'Frequency.eats.chicken.or.meat', 'Frequency.eats.fried.food',
       'Frequency.takes.aerated.drinks','Frequency.household.members.smoke.inside.the.house','Wealth.index',
       'Highest.educational.level', 'Current.age','BMI','Hemoglobin.level..g.dl...1.decimal.','Time.to.get.to.water.source..minutes.', 'Household.head.s.religion', 'Sex', 'Type.of.place.of.residence', 'Household.structure',
       'Type.of.caste.or.tribe.of.the.household.head','Type.of.cooking.fuel','Source.of.drinking.water']]

Function for dimension reduction using UMAP¶

In [8]:
def feature_clustering(UMAP_neb,min_dist_UMAP, metric, data, visual):
    import umap.umap_ as umap
    np.random.seed(42)
    data_embedded = umap.UMAP(n_neighbors=UMAP_neb, min_dist=min_dist_UMAP, n_components=2, metric=metric, random_state=42).fit_transform(data)
    data_embedded[:,0]=(data_embedded[:,0]- np.mean(data_embedded[:,0]))/np.std(data_embedded[:,0])
    data_embedded[:,1]=(data_embedded[:,1]- np.mean(data_embedded[:,1]))/np.std(data_embedded[:,1])
    result = pd.DataFrame(data = data_embedded , 
        columns = ['UMAP_0', 'UMAP_1'])
    if visual==1:
        sns.lmplot( x="UMAP_0", y="UMAP_1",data=result,fit_reg=False,legend=False,scatter_kws={"s": 3},palette=customPalette_set1) # specify the point size
        #plt.savefig('clusters_umap_all.png', dpi=700, bbox_inches='tight')
        plt.show()
    else:
        pass
    return result

Dividing features¶

  • ord_list=ordinal features
  • cont_list=continueous features
  • nom_list=nominal features
In [9]:
ord_list=['Drinks.alcohol', 'Smoking_stat','Has.refrigerator',
       'Has.bicycle', 'Has.motorcycle.scooter', 'Has.car.truck', 'Owns.livestock..herds.or.farm.animals','Frequency.takes.milk.or.curd',
       'Frequency.eats.pulses.or.beans',
       'Frequency.eats.dark.green.leafy.vegetable', 'Frequency.eats.fruits',
       'Frequency.eats.eggs', 'Frequency.eats.fish',
       'Frequency.eats.chicken.or.meat', 'Frequency.eats.fried.food',
       'Frequency.takes.aerated.drinks','Frequency.household.members.smoke.inside.the.house','Wealth.index',
       'Highest.educational.level' ]
cont_list=['Current.age','BMI','Hemoglobin.level..g.dl...1.decimal.','Time.to.get.to.water.source..minutes.']
nom_list=['Household.head.s.religion', 'Sex', 'Type.of.place.of.residence', 'Household.structure',
       'Type.of.caste.or.tribe.of.the.household.head','Type.of.cooking.fuel','Source.of.drinking.water']

Function for Feature-type Distributed Clustering (FDC)¶

Function parameters:¶

  • data=dataframe on which feature distributed clustering should be performed
  • cont_list=list of continueous features
  • nom_list=list of nominal features
  • ord_list=list of ordinal features
  • cont_metric=distance metric for continueous data
  • ord_metric=distance metric for ordinal data
  • nom_metric=distance metric for nominal data
  • drop_nominal=1(to drop nominal data) or 0(don't drop nominal data)
  • visual=1(to plot the data) or 0(don't plot the data)
In [10]:
def FDC(data,cont_list,nom_list,ord_list,cont_metric, ord_metric, nom_metric, drop_nominal, visual):
    np.random.seed(42)
    colors_set1 = ["lightcoral", "lightseagreen", "mediumorchid", "orange", "burlywood", "cornflowerblue", "plum", "yellowgreen"]
    customPalette_set1 = sns.set_palette(sns.color_palette(colors_set1))
    cont_df=data[cont_list]
    nom_df=data[nom_list]
    ord_df=data[ord_list]
    cont_emb=feature_clustering(30,0.1, cont_metric, cont_df, 0) #Reducing continueous features into 2dim
    ord_emb=feature_clustering(30,0.1, ord_metric, ord_df, 0) #Reducing ordinal features into 2dim
    nom_emb=feature_clustering(30,0.1, nom_metric, nom_df, 0) #Reducing nominal features into 2dim
    if drop_nominal==1:
        result_concat=pd.concat([ord_emb.drop(['UMAP_1'],axis=1), cont_emb.drop(['UMAP_1'],axis=1), nom_emb.drop(['UMAP_1'],axis=1)],axis=1) #concatinating all reduced dimensions to get 5D embedding(1D from nominal)
    else:
        result_concat=pd.concat([ord_emb, cont_emb, nom_emb],axis=1)
    data_embedded = umap.UMAP(n_neighbors=30, min_dist=0.001, n_components=2, metric='euclidean', random_state=42).fit_transform(result_concat) #reducing 5D embedding to 2D using UMAP
    result_reduced = pd.DataFrame(data = data_embedded , 
        columns = ['UMAP_0', 'UMAP_1'])
    
    if visual==1:
        sns.lmplot( x="UMAP_0", y="UMAP_1",data=result_reduced,fit_reg=False,legend=False,scatter_kws={"s": 3},palette=customPalette_set1) # specify the point size
        plt.show()
        #plt.savefig('clusters_umap_all.png', dpi=700, bbox_inches='tight')
    else:
        pass
    return result_concat, result_reduced #returns both 5D and 2D embedding
In [11]:
# applying Feature Distributed Clustering(FDC) on entire 10125 data with all features except disease features
entire_data_FDC_emb_three,entire_data_FDC_emb_two=FDC(data_others,cont_list,nom_list,ord_list,'euclidean','canberra','hamming',1,1)
2022-08-17T16:09:27.754029 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/

DBSCAN clustering on FDC embedding¶

In [12]:
def db_scan(eps,min_samples,five_d_embedding,two_d_embedding,visual, pal):
    from sklearn.cluster import DBSCAN
    dbscan = DBSCAN(eps=eps, min_samples = min_samples)
    clusters=dbscan.fit_predict(five_d_embedding)
    (values,counts) = np.unique(clusters,return_counts=True)
    two_d_embedding['Cluster'] = clusters
    
    if visual==1:
        sns.lmplot( x="UMAP_0", y="UMAP_1",
        data=two_d_embedding,
        fit_reg=False, 
        legend=True,
        hue='Cluster', # color by cluster
        scatter_kws={"s": 3},palette=pal) # specify the point size
        plt.savefig('dbscan_ref_3dim.png', dpi=700, bbox_inches='tight')
        plt.show()
    else:
        pass
    return two_d_embedding.Cluster.to_list(),counts
In [13]:
#setting color palette for visualization of clusters
colors_set1 = ['lightgray','lightcoral','cornflowerblue','orange','mediumorchid', 'lightseagreen','olive', 'chocolate','steelblue']
customPalette_set1 = sns.set_palette(sns.color_palette(colors_set1))


#Applying clustering algorithm on FDC embedding from entire data
entire_data_cluster_list,entire_data_cluster_counts=db_scan(0.5,140,entire_data_FDC_emb_three,entire_data_FDC_emb_two,1,customPalette_set1)
2022-08-17T16:09:29.769262 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/
In [14]:
#Getting noise indices
non_noise_indices= np.where(np.array(entire_data_cluster_list)!=-1)

#Removing noise/outlires from FDC embedding and from entire data
entire_data_FDC_emb_three= entire_data_FDC_emb_three.iloc[non_noise_indices]
entire_data_FDC_emb_two= entire_data_FDC_emb_two.iloc[non_noise_indices]
entire_data_cluster_list= np.array(entire_data_cluster_list)[non_noise_indices]
data_others= data_others.iloc[non_noise_indices]

#Creating new cloumn for storing cluster labels 
data_others['cluster_labels']= entire_data_cluster_list

#getting binary representation for cluster labels
data_others= pd.get_dummies(data=data_others, columns=['cluster_labels'])
In [15]:
#Getting column names of encoded cluster labels
cluster_column_names=data_others.columns[-len(np.unique(entire_data_cluster_list)):].to_list()

Dividing data set for experiments¶

In [16]:
#75%  of entire data for training
np.random.seed(42)
data=data_others.sample(frac=0.75) # Training data
In [17]:
#Another 25% of entire data for validation
np.random.seed(42)
data_val=data_others.drop(data.index) # Validation data

Dividing training data into 3 folds¶

In [18]:
#Dividing training data into three folds

np.random.seed(42)
df_1=data.sample(frac=0.33) #fold 1

df=data.drop(df_1.index)
df_2=df.sample(frac=0.51) #fold 2

df_3=df.drop(df_2.index) #fold 3
In [19]:
np.random.seed(42)
#Possible combinations of concating 2 folds for training and using remaining fold for testing
training_folds=[pd.concat([df_1,df_2],axis=0), pd.concat([df_2,df_3],axis=0), pd.concat([df_3,df_1],axis=0)]
testing_folds=[df_3,df_1,df_2]

Function for neural network¶

Function parameters:¶

  • n_features= dimension of input data
  • hidden_dim1= dimension of first hidden layer
  • hidden_dim2= dimension of second hidden layer
  • out_emb_size= dimension of output data
  • act1= first hidden layer activation function
  • act2= second hidden layer activation function
In [20]:
def neural_network(n_features,hidden_dim1,hidden_dim2,out_emb_size,act1,act2,loss):
    np.random.seed(42)
    tf.random.set_seed(42)
    model=keras.Sequential([
         keras.layers.Dense(hidden_dim1,input_dim=n_features,activation=act1),
         keras.layers.Dense(hidden_dim1,activation=act2),
         keras.layers.Dense(out_emb_size)])
    model.compile(optimizer="adam" ,
              loss=loss, 
              metrics=['mse'])
    return model

Function for Cluster Incidence Matrix (CIM)¶

  • creating a matrix to evaluate the performance based on predicted cluster labels
In [21]:
def cluster_incidence_matrix_mod(cluster_list_new):
    np.random.seed(42)
    
    matrix=np.zeros((len(cluster_list_new),len(cluster_list_new)))
    for i in range(len(cluster_list_new)):
        for j in range(len(cluster_list_new)):
                if cluster_list_new[i]==cluster_list_new[j]:
                    matrix[i,j]=1 
                else:
                    pass
    
    return matrix
In [22]:
#Function for decoding the encoded cluster labels
def label_decoder(label_dataframe):
    label_array=np.array(label_dataframe)
    decoded_labels=[]
    for i in label_array:
        max_val=np.argmax(i)
        decoded_labels.append(max_val)
    return decoded_labels
In [23]:
colnames=[]
for i in range(len(entire_data_FDC_emb_three.columns)):
    colnames.append('c'+str(i+1))
In [24]:
np.random.seed(42)
count=0
fold_readings=[]
while count<3:
    FDC_emb_three_train=entire_data_FDC_emb_three.loc[list(training_folds[count].index)] #3D FDC embedding of training folds from entire training data
    FDC_emb_two_train=entire_data_FDC_emb_two.loc[list(training_folds[count].index)] #2D embedding of training folds from entire training data
    FDC_emb_three_train.columns=colnames
    
    #Thirty dimensional data of training fold as features_matrix(X_train) 
    features_matrix=np.array(training_folds[count].drop(cluster_column_names, axis=1,inplace=False)) #X_train
    
    #three dimensional FDC embedding of training fold as target_matrix(y_train)
    target_matrix=np.array(FDC_emb_three_train) #y_train
    
    #Train a neural network to get five dimensional embedding
    model_1=neural_network(len(features_matrix[0]),int(0.6*len(features_matrix[0])),int(0.36*len(features_matrix[0])),len(target_matrix[0]),"relu","sigmoid","mse")
    history=model_1.fit(features_matrix,target_matrix,epochs=30,batch_size=8)
    print('\n')
    print('Training history across epochs for fold ',count+1)
    plt.plot(history.history['mse'],'r')
    plt.ylabel('mse')
    plt.xlabel('epoch')
    plt.show()
    
    #Using same thirty dimensional features_matrix(X_train) from first neural network and encoded cluster labels of training fold as target_labels_matrix(y_train) 
    target_labels_matrix=np.array(training_folds[count].loc[:,cluster_column_names]) #y
    
    
    #Train a neural network to get encoded cluster labels
    model_2=neural_network(len(features_matrix[0]),int(0.6*len(features_matrix[0])),int(0.36*len(features_matrix[0])),len(target_labels_matrix[0]),"relu","softmax","mse")
    history=model_2.fit(features_matrix,target_labels_matrix,epochs=30,batch_size=8)
    print('\n')
    print('Training history across epochs for fold ',count+1)
    plt.plot(history.history['mse'],'r')
    plt.ylabel('mse')
    plt.xlabel('epoch')
    plt.show()
    
    #Decoding cluster labels of training fold
    decoded_target_labels_matrix=label_decoder(target_labels_matrix)

    #Actual encoded cluster labels of testing fold for metric calculation  
    ref_clusters=testing_folds[count].loc[:,cluster_column_names] 
    #Decoding encoded cluster labels of testing fold
    decoded_ref_clusters=label_decoder(ref_clusters)
    

    #predicting testing fold to get three dim embedding using trained model_1
    testing_data=testing_folds[count].drop(cluster_column_names, axis=1,inplace=False)
    predicted_3dim=pd.DataFrame(model_1.predict(testing_data), columns=colnames)
    
    #UMAP on predicted 3D embedding
    predicted_2dim=feature_clustering(30,0.01, "euclidean", predicted_3dim, 0)

    #predicting testing fold to get encoded cluster labels using trained model_2
    predicted_clusters=pd.DataFrame(model_2.predict(testing_data))
    
    #Decoding predicted encoded cluster labels
    decoded_predicted_clusters=label_decoder(predicted_clusters)
    
    
    #concatinating training and predicted 3D embedding
    concatenated_3dim=pd.concat([FDC_emb_three_train,predicted_3dim])
    
    #UMAP on concatinated embedding
    two_dim_viz=feature_clustering(30, 0.01, 'euclidean', concatenated_3dim, 0)
    
    #Concatinating decoded cluster labels of training fold and predicted testing fold
    concatenated_cluster_labels=np.concatenate([np.array(decoded_target_labels_matrix),np.array(decoded_predicted_clusters)+len(np.unique(decoded_target_labels_matrix))])
    
    two_dim_viz['Cluster']= concatenated_cluster_labels
    
    
    #Setting dark colors for training folds    
    darkerhues=['lightcoral','cornflowerblue','orange','mediumorchid', 'lightseagreen','olive', 'chocolate','steelblue']
    colors_set2=[]
    for i in range(len(np.unique(decoded_target_labels_matrix))):
        colors_set2.append(darkerhues[i])
    
    #Concatinating dark colors for training folds and corresponding light colors for testing folds
    colors_set2=colors_set2+["lightpink", 'skyblue', 'wheat', "plum","paleturquoise",  "lightgreen",  'burlywood','lightsteelblue']
    
    print('Vizualization for FDC for training fold (shown in dark hue) '+str(count+1) + 'and predicted clusters from neural network on testing fold (shown in corresponding light hues) '+str(count+1))
    
    #visualizing the clusters of both training and testing folds
    sns.lmplot( x="UMAP_0", y="UMAP_1", data=two_dim_viz, fit_reg=False, legend=False, hue='Cluster', scatter_kws={"s": 3},palette=sns.set_palette(sns.color_palette(colors_set2))) 
    plt.show()
    
    #Metric calculation

    CIM_predicted=cluster_incidence_matrix_mod(np.array(decoded_predicted_clusters))#Cluster incidence metric for predicted clusters
    CIM_reference=cluster_incidence_matrix_mod(np.array(decoded_ref_clusters))#Cluster incidence metric for reference clusters
    Product=np.dot(CIM_predicted,CIM_reference)
    cluster_incdences_in_data=np.sum(CIM_reference,axis=1)  
    mean_points_in_same_clusters=np.mean(np.diagonal(Product)/cluster_incdences_in_data)
    fold_readings.append(mean_points_in_same_clusters*100)
    
    print("Average percentage of patients belongs to the same cluster is: {}%".format(mean_points_in_same_clusters*100))
    print('\n')
    count+=1


print('\n')
print('\n')

Epoch 1/30
538/538 [==============================] - 1s 1ms/step - loss: 0.4736 - mse: 0.4736
Epoch 2/30
538/538 [==============================] - 1s 1ms/step - loss: 0.2631 - mse: 0.2631
Epoch 3/30
538/538 [==============================] - 1s 1ms/step - loss: 0.2355 - mse: 0.2355
Epoch 4/30
538/538 [==============================] - 1s 1ms/step - loss: 0.2259 - mse: 0.2259
Epoch 5/30
538/538 [==============================] - 1s 1ms/step - loss: 0.2175 - mse: 0.2175
Epoch 6/30
538/538 [==============================] - 1s 1ms/step - loss: 0.2110 - mse: 0.2110
Epoch 7/30
538/538 [==============================] - 1s 1ms/step - loss: 0.2027 - mse: 0.2027
Epoch 8/30
538/538 [==============================] - 1s 1ms/step - loss: 0.1963 - mse: 0.1963
Epoch 9/30
538/538 [==============================] - 1s 1ms/step - loss: 0.1897 - mse: 0.1897
Epoch 10/30
538/538 [==============================] - 1s 1ms/step - loss: 0.1850 - mse: 0.1850
Epoch 11/30
538/538 [==============================] - 1s 1ms/step - loss: 0.1812 - mse: 0.1812
Epoch 12/30
538/538 [==============================] - 1s 1ms/step - loss: 0.1756 - mse: 0.1756
Epoch 13/30
538/538 [==============================] - 1s 1ms/step - loss: 0.1691 - mse: 0.1691
Epoch 14/30
538/538 [==============================] - 1s 1ms/step - loss: 0.1641 - mse: 0.1641
Epoch 15/30
538/538 [==============================] - 1s 1ms/step - loss: 0.1577 - mse: 0.1577
Epoch 16/30
538/538 [==============================] - 1s 1ms/step - loss: 0.1513 - mse: 0.1513
Epoch 17/30
538/538 [==============================] - 1s 1ms/step - loss: 0.1461 - mse: 0.1461
Epoch 18/30
538/538 [==============================] - 1s 1ms/step - loss: 0.1411 - mse: 0.1411
Epoch 19/30
538/538 [==============================] - 1s 1ms/step - loss: 0.1372 - mse: 0.1372
Epoch 20/30
538/538 [==============================] - 1s 1ms/step - loss: 0.1338 - mse: 0.1338
Epoch 21/30
538/538 [==============================] - 1s 982us/step - loss: 0.1286 - mse: 0.1286
Epoch 22/30
538/538 [==============================] - 1s 1ms/step - loss: 0.1250 - mse: 0.1250
Epoch 23/30
538/538 [==============================] - 1s 1ms/step - loss: 0.1224 - mse: 0.1224
Epoch 24/30
538/538 [==============================] - 1s 1ms/step - loss: 0.1203 - mse: 0.1203
Epoch 25/30
538/538 [==============================] - 1s 1ms/step - loss: 0.1187 - mse: 0.1187
Epoch 26/30
538/538 [==============================] - 1s 1ms/step - loss: 0.1154 - mse: 0.1154
Epoch 27/30
538/538 [==============================] - 1s 1ms/step - loss: 0.1150 - mse: 0.1150
Epoch 28/30
538/538 [==============================] - 1s 1ms/step - loss: 0.1124 - mse: 0.1124
Epoch 29/30
538/538 [==============================] - 1s 1ms/step - loss: 0.1124 - mse: 0.1124
Epoch 30/30
538/538 [==============================] - 1s 1ms/step - loss: 0.1105 - mse: 0.1105


Training history across epochs for fold  1
2022-08-17T16:09:48.947551 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/ 
Epoch 1/30
538/538 [==============================] - 1s 1ms/step - loss: 0.1126 - mse: 0.1126
Epoch 2/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0392 - mse: 0.0392
Epoch 3/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0200 - mse: 0.0200
Epoch 4/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0176 - mse: 0.0176
Epoch 5/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0170 - mse: 0.0170
Epoch 6/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0161 - mse: 0.0161
Epoch 7/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0155 - mse: 0.0155
Epoch 8/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0155 - mse: 0.0155
Epoch 9/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0148 - mse: 0.0148
Epoch 10/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0148 - mse: 0.0148
Epoch 11/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0148 - mse: 0.0148
Epoch 12/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0144 - mse: 0.0144
Epoch 13/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0142 - mse: 0.0142
Epoch 14/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0142 - mse: 0.0142
Epoch 15/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0139 - mse: 0.0139
Epoch 16/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0141 - mse: 0.0141
Epoch 17/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0139 - mse: 0.0139
Epoch 18/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0139 - mse: 0.0139
Epoch 19/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0137 - mse: 0.0137
Epoch 20/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0138 - mse: 0.0138
Epoch 21/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0137 - mse: 0.0137
Epoch 22/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0138 - mse: 0.0138
Epoch 23/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0135 - mse: 0.0135
Epoch 24/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0138 - mse: 0.0138
Epoch 25/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0132 - mse: 0.0132
Epoch 26/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0133 - mse: 0.0133
Epoch 27/30
538/538 [==============================] - 1s 973us/step - loss: 0.0133 - mse: 0.0133
Epoch 28/30
538/538 [==============================] - 1s 1ms/step - loss: 0.0132 - mse: 0.0132
Epoch 29/30
538/538 [==============================] - 1s 990us/step - loss: 0.0131 - mse: 0.0131
Epoch 30/30
538/538 [==============================] - 1s 993us/step - loss: 0.0130 - mse: 0.0130


Training history across epochs for fold  1
2022-08-17T16:10:07.449034 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/ 
66/66 [==============================] - 0s 775us/step
66/66 [==============================] - 0s 721us/step
Vizualization for FDC for training fold (shown in dark hue) 1and predicted clusters from neural network on testing fold (shown in corresponding light hues) 1
2022-08-17T16:10:29.175882 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/ 
Average percentage of patients belongs to the same cluster is: 98.02617072048253%


Epoch 1/30
536/536 [==============================] - 1s 965us/step - loss: 0.4823 - mse: 0.4823
Epoch 2/30
536/536 [==============================] - 1s 989us/step - loss: 0.2682 - mse: 0.2682
Epoch 3/30
536/536 [==============================] - 1s 994us/step - loss: 0.2362 - mse: 0.2362
Epoch 4/30
536/536 [==============================] - 1s 1ms/step - loss: 0.2262 - mse: 0.2262
Epoch 5/30
536/536 [==============================] - 1s 1ms/step - loss: 0.2182 - mse: 0.2182
Epoch 6/30
536/536 [==============================] - 1s 1ms/step - loss: 0.2120 - mse: 0.2120
Epoch 7/30
536/536 [==============================] - 1s 1ms/step - loss: 0.2056 - mse: 0.2056
Epoch 8/30
536/536 [==============================] - 1s 1ms/step - loss: 0.2002 - mse: 0.2002
Epoch 9/30
536/536 [==============================] - 1s 1ms/step - loss: 0.1939 - mse: 0.1939
Epoch 10/30
536/536 [==============================] - 1s 1ms/step - loss: 0.1891 - mse: 0.1891
Epoch 11/30
536/536 [==============================] - 1s 1ms/step - loss: 0.1833 - mse: 0.1833
Epoch 12/30
536/536 [==============================] - 1s 1ms/step - loss: 0.1781 - mse: 0.1781
Epoch 13/30
536/536 [==============================] - 1s 1ms/step - loss: 0.1738 - mse: 0.1738
Epoch 14/30
536/536 [==============================] - 1s 1ms/step - loss: 0.1694 - mse: 0.1694
Epoch 15/30
536/536 [==============================] - 1s 1ms/step - loss: 0.1641 - mse: 0.1641
Epoch 16/30
536/536 [==============================] - 1s 967us/step - loss: 0.1599 - mse: 0.1599
Epoch 17/30
536/536 [==============================] - 1s 946us/step - loss: 0.1563 - mse: 0.1563
Epoch 18/30
536/536 [==============================] - 1s 1ms/step - loss: 0.1517 - mse: 0.1517
Epoch 19/30
536/536 [==============================] - 1s 1ms/step - loss: 0.1481 - mse: 0.1481
Epoch 20/30
536/536 [==============================] - 1s 1ms/step - loss: 0.1434 - mse: 0.1434
Epoch 21/30
536/536 [==============================] - 1s 1ms/step - loss: 0.1391 - mse: 0.1391
Epoch 22/30
536/536 [==============================] - 1s 1ms/step - loss: 0.1344 - mse: 0.1344
Epoch 23/30
536/536 [==============================] - 1s 1ms/step - loss: 0.1319 - mse: 0.1319
Epoch 24/30
536/536 [==============================] - 1s 1ms/step - loss: 0.1294 - mse: 0.1294
Epoch 25/30
536/536 [==============================] - 1s 1ms/step - loss: 0.1256 - mse: 0.1256
Epoch 26/30
536/536 [==============================] - 1s 1ms/step - loss: 0.1235 - mse: 0.1235
Epoch 27/30
536/536 [==============================] - 1s 1ms/step - loss: 0.1202 - mse: 0.1202
Epoch 28/30
536/536 [==============================] - 1s 1ms/step - loss: 0.1210 - mse: 0.1210
Epoch 29/30
536/536 [==============================] - 1s 1ms/step - loss: 0.1173 - mse: 0.1173
Epoch 30/30
536/536 [==============================] - 1s 1ms/step - loss: 0.1162 - mse: 0.1162


Training history across epochs for fold  2
2022-08-17T16:10:49.313048 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/ 
Epoch 1/30
536/536 [==============================] - 1s 1ms/step - loss: 0.1092 - mse: 0.1092
Epoch 2/30
536/536 [==============================] - 1s 1ms/step - loss: 0.0338 - mse: 0.0338
Epoch 3/30
536/536 [==============================] - 1s 952us/step - loss: 0.0191 - mse: 0.0191
Epoch 4/30
536/536 [==============================] - 1s 1ms/step - loss: 0.0175 - mse: 0.0175
Epoch 5/30
536/536 [==============================] - 1s 1ms/step - loss: 0.0164 - mse: 0.0164
Epoch 6/30
536/536 [==============================] - 1s 1ms/step - loss: 0.0159 - mse: 0.0159
Epoch 7/30
536/536 [==============================] - 1s 1ms/step - loss: 0.0154 - mse: 0.0154
Epoch 8/30
536/536 [==============================] - 1s 1ms/step - loss: 0.0152 - mse: 0.0152
Epoch 9/30
536/536 [==============================] - 1s 1ms/step - loss: 0.0147 - mse: 0.0147
Epoch 10/30
536/536 [==============================] - 1s 1ms/step - loss: 0.0144 - mse: 0.0144
Epoch 11/30
536/536 [==============================] - 1s 1ms/step - loss: 0.0144 - mse: 0.0144
Epoch 12/30
536/536 [==============================] - 1s 1ms/step - loss: 0.0145 - mse: 0.0145
Epoch 13/30
536/536 [==============================] - 1s 2ms/step - loss: 0.0141 - mse: 0.0141
Epoch 14/30
536/536 [==============================] - 1s 1ms/step - loss: 0.0146 - mse: 0.0146
Epoch 15/30
536/536 [==============================] - 1s 1ms/step - loss: 0.0140 - mse: 0.0140
Epoch 16/30
536/536 [==============================] - 1s 1ms/step - loss: 0.0141 - mse: 0.0141
Epoch 17/30
536/536 [==============================] - 1s 972us/step - loss: 0.0139 - mse: 0.0139
Epoch 18/30
536/536 [==============================] - 1s 939us/step - loss: 0.0141 - mse: 0.0141
Epoch 19/30
536/536 [==============================] - 1s 981us/step - loss: 0.0139 - mse: 0.0139
Epoch 20/30
536/536 [==============================] - 1s 1ms/step - loss: 0.0141 - mse: 0.0141
Epoch 21/30
536/536 [==============================] - 1s 1ms/step - loss: 0.0135 - mse: 0.0135
Epoch 22/30
536/536 [==============================] - 1s 1ms/step - loss: 0.0137 - mse: 0.0137
Epoch 23/30
536/536 [==============================] - 1s 1ms/step - loss: 0.0136 - mse: 0.0136
Epoch 24/30
536/536 [==============================] - 1s 1ms/step - loss: 0.0139 - mse: 0.0139
Epoch 25/30
536/536 [==============================] - 1s 1ms/step - loss: 0.0134 - mse: 0.0134
Epoch 26/30
536/536 [==============================] - 1s 1ms/step - loss: 0.0138 - mse: 0.0138
Epoch 27/30
536/536 [==============================] - 1s 1ms/step - loss: 0.0138 - mse: 0.0138
Epoch 28/30
536/536 [==============================] - 1s 1ms/step - loss: 0.0138 - mse: 0.0138
Epoch 29/30
536/536 [==============================] - 1s 1ms/step - loss: 0.0135 - mse: 0.0135
Epoch 30/30
536/536 [==============================] - 1s 1ms/step - loss: 0.0134 - mse: 0.0134


Training history across epochs for fold  2
2022-08-17T16:11:08.123094 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/ 
66/66 [==============================] - 0s 799us/step
66/66 [==============================] - 0s 721us/step
Vizualization for FDC for training fold (shown in dark hue) 2and predicted clusters from neural network on testing fold (shown in corresponding light hues) 2
2022-08-17T16:11:29.092268 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/ 
Average percentage of patients belongs to the same cluster is: 97.19978443243934%


Epoch 1/30
527/527 [==============================] - 1s 1ms/step - loss: 0.4858 - mse: 0.4858
Epoch 2/30
527/527 [==============================] - 1s 1ms/step - loss: 0.2675 - mse: 0.2675
Epoch 3/30
527/527 [==============================] - 1s 977us/step - loss: 0.2390 - mse: 0.2390
Epoch 4/30
527/527 [==============================] - 1s 981us/step - loss: 0.2300 - mse: 0.2300
Epoch 5/30
527/527 [==============================] - 1s 1ms/step - loss: 0.2222 - mse: 0.2222
Epoch 6/30
527/527 [==============================] - 1s 1ms/step - loss: 0.2174 - mse: 0.2174
Epoch 7/30
527/527 [==============================] - 1s 1ms/step - loss: 0.2137 - mse: 0.2137
Epoch 8/30
527/527 [==============================] - 1s 1ms/step - loss: 0.2075 - mse: 0.2075
Epoch 9/30
527/527 [==============================] - 1s 1ms/step - loss: 0.2018 - mse: 0.2018
Epoch 10/30
527/527 [==============================] - 1s 1ms/step - loss: 0.1949 - mse: 0.1949
Epoch 11/30
527/527 [==============================] - 1s 1ms/step - loss: 0.1880 - mse: 0.1880
Epoch 12/30
527/527 [==============================] - 1s 1ms/step - loss: 0.1786 - mse: 0.1786
Epoch 13/30
527/527 [==============================] - 1s 1ms/step - loss: 0.1715 - mse: 0.1715
Epoch 14/30
527/527 [==============================] - 1s 1ms/step - loss: 0.1634 - mse: 0.1634
Epoch 15/30
527/527 [==============================] - 1s 1ms/step - loss: 0.1559 - mse: 0.1559
Epoch 16/30
527/527 [==============================] - 1s 1ms/step - loss: 0.1494 - mse: 0.1494
Epoch 17/30
527/527 [==============================] - 1s 1ms/step - loss: 0.1430 - mse: 0.1430
Epoch 18/30
527/527 [==============================] - 1s 1ms/step - loss: 0.1396 - mse: 0.1396
Epoch 19/30
527/527 [==============================] - 1s 1ms/step - loss: 0.1335 - mse: 0.1335
Epoch 20/30
527/527 [==============================] - 1s 1ms/step - loss: 0.1301 - mse: 0.1301
Epoch 21/30
527/527 [==============================] - 1s 997us/step - loss: 0.1261 - mse: 0.1261
Epoch 22/30
527/527 [==============================] - 1s 1000us/step - loss: 0.1241 - mse: 0.1241
Epoch 23/30
527/527 [==============================] - 1s 1ms/step - loss: 0.1202 - mse: 0.1202
Epoch 24/30
527/527 [==============================] - 1s 1ms/step - loss: 0.1174 - mse: 0.1174
Epoch 25/30
527/527 [==============================] - 1s 1ms/step - loss: 0.1149 - mse: 0.1149
Epoch 26/30
527/527 [==============================] - 1s 1ms/step - loss: 0.1132 - mse: 0.1132
Epoch 27/30
527/527 [==============================] - 1s 1ms/step - loss: 0.1122 - mse: 0.1122
Epoch 28/30
527/527 [==============================] - 1s 1ms/step - loss: 0.1104 - mse: 0.1104
Epoch 29/30
527/527 [==============================] - 1s 1ms/step - loss: 0.1101 - mse: 0.1101
Epoch 30/30
527/527 [==============================] - 1s 1ms/step - loss: 0.1092 - mse: 0.1092


Training history across epochs for fold  3
2022-08-17T16:11:50.184456 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/ 
Epoch 1/30
527/527 [==============================] - 1s 1ms/step - loss: 0.1096 - mse: 0.1096
Epoch 2/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0365 - mse: 0.0365
Epoch 3/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0188 - mse: 0.0188
Epoch 4/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0174 - mse: 0.0174
Epoch 5/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0163 - mse: 0.0163
Epoch 6/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0160 - mse: 0.0160
Epoch 7/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0160 - mse: 0.0160
Epoch 8/30
527/527 [==============================] - 1s 993us/step - loss: 0.0154 - mse: 0.0154
Epoch 9/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0154 - mse: 0.0154
Epoch 10/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0150 - mse: 0.0150
Epoch 11/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0148 - mse: 0.0148
Epoch 12/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0146 - mse: 0.0146
Epoch 13/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0147 - mse: 0.0147
Epoch 14/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0148 - mse: 0.0148
Epoch 15/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0144 - mse: 0.0144
Epoch 16/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0142 - mse: 0.0142
Epoch 17/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0141 - mse: 0.0141
Epoch 18/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0140 - mse: 0.0140
Epoch 19/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0140 - mse: 0.0140
Epoch 20/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0141 - mse: 0.0141
Epoch 21/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0139 - mse: 0.0139
Epoch 22/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0140 - mse: 0.0140
Epoch 23/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0140 - mse: 0.0140
Epoch 24/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0136 - mse: 0.0136
Epoch 25/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0140 - mse: 0.0140
Epoch 26/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0138 - mse: 0.0138
Epoch 27/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0137 - mse: 0.0137
Epoch 28/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0136 - mse: 0.0136
Epoch 29/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0138 - mse: 0.0138
Epoch 30/30
527/527 [==============================] - 1s 1ms/step - loss: 0.0138 - mse: 0.0138


Training history across epochs for fold  3
2022-08-17T16:12:08.833143 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/ 
69/69 [==============================] - 0s 831us/step
69/69 [==============================] - 0s 912us/step
Vizualization for FDC for training fold (shown in dark hue) 3and predicted clusters from neural network on testing fold (shown in corresponding light hues) 3
2022-08-17T16:12:30.246172 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/ 
Average percentage of patients belongs to the same cluster is: 97.12274413498312%
In [25]:
print('Average percentage of patients belonging to the same cluster over all three folds:', np.mean(np.array(fold_readings)))

Average percentage of patients belonging to the same cluster over all three folds: 97.44956642930167

Validation¶

In [26]:
np.random.seed(42)

FDC_emb_three_data=entire_data_FDC_emb_three.loc[list(data.index)] #5D FDC embedding of training fold from entire data
FDC_emb_two_data=entire_data_FDC_emb_two.loc[list(data.index)] #2D embedding of training fold from entire data
FDC_emb_three_data.columns=colnames

#Thirty dimensional data of training fold as features_matrix(X_train) 
features_matrix=np.array(data.drop(cluster_column_names, axis=1,inplace=False)) #X_train

#Five dimensional FDC embedding of training fold as target_matrix(y_train)
target_matrix=np.array(FDC_emb_three_data) #y_train

#Train a neural network to get five dimensional embedding
model_1=neural_network(len(features_matrix[0]),int(0.6*len(features_matrix[0])),int(0.36*len(features_matrix[0])),len(target_matrix[0]),"relu","sigmoid","mse")
history=model_1.fit(features_matrix,target_matrix,epochs=30,batch_size=8)
print('\n')
print('Training history across epochs for training data ')
plt.plot(history.history['mse'],'r')
plt.ylabel('mse')
plt.xlabel('epoch')
plt.show()

#Using same thirty dimensional features_matrix(X_train) from first neural network and encoded cluster labels of training fold as target_labels_matrix(y_train) 
target_labels_matrix=np.array(data.loc[:,cluster_column_names]) #y


#Train a neural network to get encoded cluster labels
model_2=neural_network(len(features_matrix[0]),int(0.6*len(features_matrix[0])),int(0.36*len(features_matrix[0])),len(target_labels_matrix[0]),"relu","softmax","mse")
history=model_2.fit(features_matrix,target_labels_matrix,epochs=30,batch_size=8)
print('\n')
print('Training history across epochs for training data ')
plt.plot(history.history['mse'],'r')
plt.ylabel('mse')
plt.xlabel('epoch')
plt.show()

#Decoding cluster labels of training fold
decoded_target_labels_matrix=label_decoder(target_labels_matrix)

#Actual encoded cluster labels of validation data for metric calculation  
ref_clusters=data_val.loc[:,cluster_column_names] 
#Decoding encoded cluster labels of validation data
decoded_ref_clusters=label_decoder(ref_clusters)


#predicting validation data to get five dim embedding using trained model_1
validation_data=data_val.drop(cluster_column_names, axis=1,inplace=False)
predicted_3dim=pd.DataFrame(model_1.predict(validation_data), columns=colnames)

#UMAP on predicted 5D embedding
predicted_2dim=feature_clustering(30,0.01, "euclidean", predicted_3dim, 0)

#predicting validation data to get encoded cluster labels using trained model_2
predicted_clusters=pd.DataFrame(model_2.predict(validation_data))

#Decoding predicted encoded cluster labels
decoded_predicted_clusters=label_decoder(predicted_clusters)


#concatinating training and predicted 5D embedding
concatenated_3dim=pd.concat([FDC_emb_three_data,predicted_3dim])

#UMAP on concatinated embedding
two_dim_viz=feature_clustering(30, 0.01, 'euclidean', concatenated_3dim, 0)

#Concatinating decoded cluster labels of training data and predicted validation data
concatenated_cluster_labels=np.concatenate([np.array(decoded_target_labels_matrix),np.array(decoded_predicted_clusters)+len(np.unique(decoded_target_labels_matrix))])

two_dim_viz['Cluster']= concatenated_cluster_labels



#Setting dark colors for training data    
darkerhues=['lightcoral','cornflowerblue','orange','mediumorchid', 'lightseagreen','olive', 'chocolate','steelblue']
colors_set2=[]
for i in range(len(np.unique(decoded_target_labels_matrix))):
    colors_set2.append(darkerhues[i])

#Concatinating dark colors for training data and corresponding light colors for validation data
colors_set2=colors_set2+["lightpink", 'skyblue', 'wheat', "plum","paleturquoise",  "lightgreen",  'burlywood','lightsteelblue']

print('Vizualization for FDC for training data (shown in dark hue) '+ 'and predicted clusters from neural network on validation data (shown in corresponding light hues) ')

#visualizing the clusters of both training and validation data
sns.lmplot( x="UMAP_0", y="UMAP_1", data=two_dim_viz, fit_reg=False, legend=False, hue='Cluster', scatter_kws={"s": 3},palette=sns.set_palette(sns.color_palette(colors_set2))) 
plt.show()

#Metric calculation

CIM_predicted=cluster_incidence_matrix_mod(np.array(decoded_predicted_clusters))#Cluster incidence metric for predicted clusters
CIM_reference=cluster_incidence_matrix_mod(np.array(decoded_ref_clusters))#Cluster incidence metric for reference clusters
Product=np.dot(CIM_predicted,CIM_reference)
cluster_incidences_in_data=np.sum(CIM_reference,axis=1)  
mean_points_in_same_clusters=np.mean(np.diagonal(Product)/cluster_incidences_in_data)
fold_readings.append(mean_points_in_same_clusters*100)

print("Average percentage of patients belongs to the same cluster is: {}%".format(mean_points_in_same_clusters*100))
print('\n')



print('\n')
print('\n')

Epoch 1/30
800/800 [==============================] - 1s 999us/step - loss: 0.4169 - mse: 0.4169
Epoch 2/30
800/800 [==============================] - 1s 1ms/step - loss: 0.2428 - mse: 0.2428
Epoch 3/30
800/800 [==============================] - 1s 1ms/step - loss: 0.2264 - mse: 0.2264
Epoch 4/30
800/800 [==============================] - 1s 2ms/step - loss: 0.2173 - mse: 0.2173
Epoch 5/30
800/800 [==============================] - 1s 1ms/step - loss: 0.2107 - mse: 0.2107
Epoch 6/30
800/800 [==============================] - 1s 1ms/step - loss: 0.2046 - mse: 0.2046
Epoch 7/30
800/800 [==============================] - 1s 991us/step - loss: 0.1972 - mse: 0.1972
Epoch 8/30
800/800 [==============================] - 1s 1ms/step - loss: 0.1894 - mse: 0.1894
Epoch 9/30
800/800 [==============================] - 1s 1ms/step - loss: 0.1802 - mse: 0.1802
Epoch 10/30
800/800 [==============================] - 1s 1ms/step - loss: 0.1716 - mse: 0.1716
Epoch 11/30
800/800 [==============================] - 1s 1ms/step - loss: 0.1638 - mse: 0.1638
Epoch 12/30
800/800 [==============================] - 1s 1ms/step - loss: 0.1576 - mse: 0.1576
Epoch 13/30
800/800 [==============================] - 1s 1ms/step - loss: 0.1518 - mse: 0.1518
Epoch 14/30
800/800 [==============================] - 1s 1ms/step - loss: 0.1458 - mse: 0.1458
Epoch 15/30
800/800 [==============================] - 1s 1ms/step - loss: 0.1420 - mse: 0.1420
Epoch 16/30
800/800 [==============================] - 1s 961us/step - loss: 0.1376 - mse: 0.1376
Epoch 17/30
800/800 [==============================] - 1s 967us/step - loss: 0.1332 - mse: 0.1332
Epoch 18/30
800/800 [==============================] - 1s 1ms/step - loss: 0.1304 - mse: 0.1304
Epoch 19/30
800/800 [==============================] - 1s 1ms/step - loss: 0.1272 - mse: 0.1272
Epoch 20/30
800/800 [==============================] - 1s 1ms/step - loss: 0.1237 - mse: 0.1237
Epoch 21/30
800/800 [==============================] - 1s 1ms/step - loss: 0.1202 - mse: 0.1202
Epoch 22/30
800/800 [==============================] - 1s 1ms/step - loss: 0.1173 - mse: 0.1173
Epoch 23/30
800/800 [==============================] - 1s 1ms/step - loss: 0.1158 - mse: 0.1158
Epoch 24/30
800/800 [==============================] - 1s 1ms/step - loss: 0.1132 - mse: 0.1132
Epoch 25/30
800/800 [==============================] - 1s 1ms/step - loss: 0.1114 - mse: 0.1114
Epoch 26/30
800/800 [==============================] - 1s 1ms/step - loss: 0.1098 - mse: 0.1098
Epoch 27/30
800/800 [==============================] - 1s 1ms/step - loss: 0.1088 - mse: 0.1088
Epoch 28/30
800/800 [==============================] - 1s 1ms/step - loss: 0.1073 - mse: 0.1073
Epoch 29/30
800/800 [==============================] - 1s 1ms/step - loss: 0.1056 - mse: 0.1056
Epoch 30/30
800/800 [==============================] - 1s 990us/step - loss: 0.1063 - mse: 0.1063


Training history across epochs for training data
2022-08-17T16:13:01.880292 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/ 
Epoch 1/30
800/800 [==============================] - 1s 969us/step - loss: 0.0944 - mse: 0.0944
Epoch 2/30
800/800 [==============================] - 1s 960us/step - loss: 0.0228 - mse: 0.0228
Epoch 3/30
800/800 [==============================] - 1s 947us/step - loss: 0.0174 - mse: 0.0174
Epoch 4/30
800/800 [==============================] - 1s 940us/step - loss: 0.0163 - mse: 0.0163
Epoch 5/30
800/800 [==============================] - 1s 1ms/step - loss: 0.0160 - mse: 0.0160
Epoch 6/30
800/800 [==============================] - 1s 1ms/step - loss: 0.0153 - mse: 0.0153
Epoch 7/30
800/800 [==============================] - 1s 980us/step - loss: 0.0150 - mse: 0.0150
Epoch 8/30
800/800 [==============================] - 1s 941us/step - loss: 0.0148 - mse: 0.0148
Epoch 9/30
800/800 [==============================] - 1s 962us/step - loss: 0.0148 - mse: 0.0148
Epoch 10/30
800/800 [==============================] - 1s 958us/step - loss: 0.0145 - mse: 0.0145
Epoch 11/30
800/800 [==============================] - 1s 940us/step - loss: 0.0146 - mse: 0.0146
Epoch 12/30
800/800 [==============================] - 1s 958us/step - loss: 0.0142 - mse: 0.0142
Epoch 13/30
800/800 [==============================] - 1s 1ms/step - loss: 0.0144 - mse: 0.0144
Epoch 14/30
800/800 [==============================] - 1s 1ms/step - loss: 0.0141 - mse: 0.0141
Epoch 15/30
800/800 [==============================] - 1s 1ms/step - loss: 0.0140 - mse: 0.0140
Epoch 16/30
800/800 [==============================] - 1s 1ms/step - loss: 0.0139 - mse: 0.0139
Epoch 17/30
800/800 [==============================] - 1s 1ms/step - loss: 0.0140 - mse: 0.0140
Epoch 18/30
800/800 [==============================] - 1s 997us/step - loss: 0.0138 - mse: 0.0138
Epoch 19/30
800/800 [==============================] - 1s 1ms/step - loss: 0.0138 - mse: 0.0138
Epoch 20/30
800/800 [==============================] - 1s 1ms/step - loss: 0.0138 - mse: 0.0138
Epoch 21/30
800/800 [==============================] - 1s 1ms/step - loss: 0.0138 - mse: 0.0138
Epoch 22/30
800/800 [==============================] - 1s 1ms/step - loss: 0.0138 - mse: 0.0138
Epoch 23/30
800/800 [==============================] - 1s 1ms/step - loss: 0.0136 - mse: 0.0136
Epoch 24/30
800/800 [==============================] - 1s 1ms/step - loss: 0.0138 - mse: 0.0138
Epoch 25/30
800/800 [==============================] - 1s 1ms/step - loss: 0.0136 - mse: 0.0136
Epoch 26/30
800/800 [==============================] - 1s 1ms/step - loss: 0.0136 - mse: 0.0136
Epoch 27/30
800/800 [==============================] - 1s 1ms/step - loss: 0.0137 - mse: 0.0137
Epoch 28/30
800/800 [==============================] - 1s 1ms/step - loss: 0.0136 - mse: 0.0136
Epoch 29/30
800/800 [==============================] - 1s 1ms/step - loss: 0.0135 - mse: 0.0135
Epoch 30/30
800/800 [==============================] - 1s 1ms/step - loss: 0.0135 - mse: 0.0135


Training history across epochs for training data
2022-08-17T16:13:27.107512 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/ 
67/67 [==============================] - 0s 710us/step
67/67 [==============================] - 0s 709us/step
Vizualization for FDC for training data (shown in dark hue) and predicted clusters from neural network on validation data (shown in corresponding light hues)
2022-08-17T16:13:50.562152 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/ 
Average percentage of patients belongs to the same cluster is: 97.18515456198324%